Saturday, December 11, 2010

The map of the world is a familiar image. But a closer look at this one reveals that it is lacking detail. For example, a number of large islands are absent, including the British Isles, Japan, and the island where I grew up, Newfoundland. The continent of Antarctica has been omitted. Furthermore, Greenland and Ellesmere Island are joined, while North and South America are disconnected. Still, the map does give a general idea of the shape of the continents (except of course Antarctica). And it's certainly better than I could draw! The map is a simplification. But is it an oversimplification?

Here I want to take a general look at oversimplification because it has broad relevance and raises some subtle questions. Maps provide a convenient example and raise some issues that turn up elsewhere. In particular, I'm going to focus on how oversimplified ideas gain traction in our society, as illustrated by three popular nonfiction books.

Although the world map above simplifies a number of details, it is important to note that any map at a given scale involves simplification. Fine detail is sacrificed for an overall description. What's more, regardless of the projection used, any two-dimensional world map inevitably provides a distorted representation of our planet. A map is a model, and as I argued previously, one should not confuse models with reality, or in the words of Alfred Korzybski, "the map is not the territory." It is however convenient to represent the world in two dimensions with various details simplified. This is a general aspect of simplification: for all its costs, it is convenient.

Nevertheless, we do have the word "oversimplification", suggesting that you can have too much of a good thing. But if that is true, where would you draw the line? How much simplification is too much simplification? This issue arises, for example, in science teaching. If you were to teach 10-year-old children about Einstein's theory of special relativity, some simplification would be necessary. If you were teaching 16-year-old children, simplification would also be necessary, but to a slightly lesser degree. Einstein himself recognized the challenge of simplification, and is often quoted as having said that "Everything should be made as simple as possible, but no simpler," which has been dubbed "Einstein's razor" in reference to Occam's Razor. Certainly, it would be oversimplification if one taught a university student the same way as a 10-year-old (or "undersimplification" if it were the other way around, though nobody uses the term).

But "oversimplification" is often used in a slightly different sense, one that hints at distortion, deception, or dishonesty. The issue then may not be too much simplification, but rather that the simplification is carried out in a way that is somehow improper. The world map above may perhaps offer a hint of this. As I noted above, some substantial islands have been omitted from the map. But larger ones such as Madagascar are present. However, one enormous landmass is not present: Antarctica, despite the fact that it is larger in land area than Australia. A possible explanation is that Antarctica is seen as unimportant because nobody lives there (except for a handful of scientists). This could be seen as a type of bias. It is one thing to simplify, but another to do so in such a way as to systematically misrepresent. I'm not really taking the map-maker to task here so much as using this as an illustration of a biased simplification.

I believe there is another way in which simplification can be improper, and that is when there is a lack of transparency. A simplified portrayal should not be presented without some explanation of how it was obtained. This provides some protection from confusing a simplification with "the truth". For example, in the case of a world map, different projections can give strikingly different impressions of our planet. For example, compare the map at the beginning of this article with the Eisenlohr conformal projection below:

Oversimplification in popular works of nonfiction

To further explore oversimplification, I'd like to consider three recent works of nonfiction. My purpose here is not to provide detailed reviews or commentary, nor to pass any overall judgment, but rather to explore issues of oversimplification that have been raised by others.

The Moral Landscape: How Science Can Determine Human Values

Sam Harris' The Moral Landscape makes the claim that moral questions can be not only informed but answered by science. Sam Harris proposes an updated version of utilitarianism, whereby an action is only morally right if it contributes to "well-being". Versions of this idea have been around for a long time: some of the key contributions to utilitarianism were made in the 1800's, and numerous objections and counterarguments have been made since then. But as Kwame Anthony Appiah writes in the New York Times, "having acknowledged some of these complications, [Harris] is inclined to push them aside and continue down his path." As philosophy professor Troy Jollimore wrote:

Harris might be right that the best way to reach a "wider audience" is to sidestep difficult philosophical issues. But just how helpful to that wider audience can a book be that hides from the complexities of its subject, and misrepresents what it alleges to discuss by making genuinely difficult questions look straightforward and simple?

As I noted earlier, misrepresented simplification is a key feature of oversimplification. Harris has also been criticized for using an uncommonly broad definition of science and for placing it in an easily-missed footnote. The footnote reads:

For the purposes of this discussion, I do not intend to make a hard distinction between “science” and other intellectual contexts in which we discuss “facts”—e.g., history. For instance, it is a fact that John F. Kennedy was assassinated. Facts of this kind fall within the context of “science,” broadly construed as our best effort to form a rational account of empirical reality. Granted, one doesn’t generally think of events like assassinations as “scientific” facts, but the murder of President Kennedy is as fully corroborated a fact as can be found anywhere, and it would betray a profoundly unscientific frame of mind to deny that it occurred. I think “science,” therefore, should be considered a specialized branch of a larger effort to form true beliefs about events in our world.

It does seem odd to put in a footnote an idiosyncratic definition of a word that appears in the book's subtitle and is central to Harris' case. Note that Harris' use of a generalized notion of science is a form of simplification. Failing to highlight this simplification could be seen as oversimplification.

The Tipping Point: How Little Things Can Make a Big Difference

Malcolm Gladwell's The Tipping Point explores factors that may explain how social trends can suddenly catch on. In a review on Amazon.com, Benjamin Northrop wrote that Gladwell "seems to be showing you what's really behind the "curtain" - not something boring or muddled or technical, but rather something simple and crisp and clear!" He goes on to say that

The problem, however, is that real life is not so simple, nor is real science. Complex phenomenon have complex causal components. ... Gladwell, however, disingenuously presents only the facts and the stories that prove his point, giving the reader the false impression that there really is no debate, he has found "the answer".

Northrup's mention of "complex causal components" points to causal oversimplification. Many phenomena have multiple causes; reducing them to a single purported mechanism can make for a more compelling account, but may provide only a counterfeit understanding.

The Blank Slate: The Modern Denial of Human Nature

Stephen Pinker's The Blank Slate attacks the nurture side of the nature-nurture debate. In a review, David B Richman suggests that Pinker has constructed a straw man:

I agree with [Pinker] that a person's genetic makeup is highly important and that the extreme blank slate idea (that humans are born without a human nature and can be "written on" like a blank slate) is obviously wrong. ... However, I cannot follow the equally extreme idea that only our genes matter (a concept that Pinker alternately defends and retreats from.) As several people have pointed out in recent research the expression of a gene is primarily a dialog between genome and environment. Indeed, is there any reputable scientist today who believes in the absolute Blank Slate?

A straw man is a kind of oversimplification: the wide range of views on a topic that are contrary to one's own are simplified down to a single, extreme one. If debate were really so polarized this might be acceptable, but this is rarely the case. And when countering an extreme opponent (albeit of one's own creation), one may find oneself presenting highly selective evidence, another hallmark of oversimplification. Another reviewer, D. Palmer, writes:

Pinker presents other points of view only in caricature, apparently with the goal of persuading the reader, not informing him.

The sources of oversimplification

Oversimplified ideas abound. All three of the above books have made it to the New York Times Bestseller lists. Politicians routinely deal in oversimplification, and the voting public often seems only too happy to accept it. Stereotypes and sweeping generalizations are ever popular. Clearly there's something very appealing about oversimplification. But as I have argued above, it is possible, through transparency and efforts to avoid bias, to separate simplification—which is not only helpful but essential—from oversimplification.

So why is oversimplification so prevalent? One reason may be that it takes much less intellectual effort to accept a simplification that is presented without a transparent explanation of how it was obtained. It is easier to point to a map and say "this is the Earth" than to say "this is a projection of the Earth onto two dimensions that exaggerates land areas near the poles". A map is most useful when we accept its metaphor, just as a play is most enjoyable when we suspend our disbelief. But to read a map intelligently you need to see the limits of the metaphor, just as a theater critic needs to be able to see the actors and not just the characters they play. This takes effort, and it is easier to simply be swept along without question.

Working overtime to overcome oversimplification

The desire for simplicity seems to be universal. But we need not be taken in by oversimplification—whether it comes from our own thoughts or from the culture around us. We can start by distinguishing simplification from oversimplification. If there is a lack of transparency it's likely that oversimplification is at work.

To prevent simplification from slipping into oversimplification, we can cultivate the discipline of switching perspectives. On the one hand, to realize the value of simplification we need to pretend that our model is "true", and work under this pretense. But on the other hand, we need to recognize the model for what it is, a convenient tool, but a construct, not reality. From this perspective we can see the limits of the model, and appreciate where it may lead us astray. Repeatedly switching perspectives, and integrating the resulting insights, is very hard work, but I believe it's essential if we want to avoid being imprisoned by our models.

I will conclude with a quote from Goethe: "Everything is simpler than you think and at the same time more complex than you can imagine."